A233767 Prime(n), where n is such that (Sum_{i=1..n} prime(i)^19) / n is an integer.

2, 97, 3203, 5059, 6469, 8081, 35051, 39719, 42209, 109049, 154591, 523297, 6621827, 20059771, 258196441, 731584957, 1427109029, 1899496631, 8428550519, 50790885203, 7475902096387, 22626378502139, 38855796912367, 162082298018497, 589085299527401, 4271778258271487

Offset: 1

Author

Robert Price, Dec 15 2013

Keywords

• nonn
• less

Comments

a(26) > 661876608760109. - Bruce Garner, Jun 30 2021

a(27) > 18205684894350047. - Paul W. Dyson, Dec 31 2024

Examples

			97 is a term, because 97 is the 25th prime and the sum of the first 25 primes^19 = 71486619210134792705255313675343157050 when divided by 25 equals 2859464768405391708210212547013726282 which is an integer.
		

Links

• OEIS Wiki, Sums of powers of primes divisibility sequences

Crossrefs

Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).

Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.

Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.

Programs

Mathematica

t = {}; sm = 0; Do[sm = sm + Prime[n]^19; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)

PARI

is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^19); s==0 \\ Charles R Greathouse IV, Nov 30 2013

PARI

my(S=n=0);forprime(p=1,,(S+=p^19)%n++||print1(p", ")) \\ M. F. Hasler, Dec 01 2013

Formula

a(n) = prime(A131279(n)).

Extensions

a(21) from Karl-Heinz Hofmann, Feb 24 2021

a(22) from Bruce Garner, Mar 01 2021

a(23) from Bruce Garner, Mar 08 2021

a(24) from Bruce Garner, Apr 14 2021

a(25) from Bruce Garner, Jun 30 2021

a(26) from Paul W. Dyson, Jun 27 2023